Introduction

Newtonian mechanics describes the macro-world correctly. However, when it is applied to describe atomic particles of very high energies, or travelling at very high speeds, it gives predictions which disagree with experiments. The absoluteness of mass, length and time were discarded by the theory of relativity – it was theorized that they depend on reference frames. Though variations of mass, length and time with speed are too small to be observed in day-to-day life, their variations are clearly observable in the world of high energy atomic particles. In the special theory of relativity, gravitational effects and accelerated motions are beyond consideration and they are dealt with in the general theory of relativity. The theory of relativity is beyond the perception of common sense. It is our duty as students of science and engineering to change our minds to fit nature, not to change nature to fit the preconceptions in our minds.

Frame of Reference

To describe a physical event, we must establish a frame of reference. The motion of a body can only be described relative to some other bodies, observers, or a set of space– time coordinates. These are called frames of reference. If the coordinates are not chosen properly, the laws of physics may be unnecessarily more complicated.

Inertial frame of reference

The reference frame in which the law of inertia (Newton's first law) holds good is called the inertial frame of reference. All inertial frames are in a state of constant, rectilinear motion with respect to one another; they do not accelerate. They may be at rest. No experiment can be performed to know whether an isolated inertial frame of reference is in motion or at rest. In an inertial frame of reference, an object is observed to have no acceleration when no forces act on it. Furthermore, any frame moving with constant velocity with respect to an inertial frame must also be an inertial frame. Measurements in one inertial frame can be converted to measurements in another by the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity. Earth is approximately taken to be an inertial reference frame. No preferred inertial reference frame exists and all inertial reference frames are equivalent.

Non-inertial frame of reference

Opposite of the inertial frame of reference is the non-inertial frame of reference or accelerated frame of reference.

Introduction

In a homogeneous medium, light travels in a straight line – if an object is placed in its path, it should cast a sharp shadow of the object. However, the shadow of a fine wire caused by sunlight is not observable on a screen and the shadow of a straight edge as shown in Fig. 3.1 is not sharp when observed minutely. Some light bends into the shadow of the straight edge with the intensity of the light decreasing rapidly as we move into the shadow. The amount of bending depends upon the wavelength of the light and the size of the obstacle. In the region of the fuzzy boundary of the shadow of the straight edge, alternate dark and bright fringes of unequal spacings are seen when viewed by a well-focused microscope against a good contrast background. This optical phenomenon of bending of light around the obstacle is called diffraction and the fringes are called diffraction bands.

The diffraction phenomenon was first discovered by Italian scientist Grimaldi in the year 1665 and was correctly interpreted by Fresnel. He combined the Huygens’ principle of secondary wavelets with the principle of interference and concluded that diffraction occurs due to the interference of secondary wavelets originating from various points of the wavefront which are not obstructed by the obstacle. The diffraction phenomenon occurs only when a part of the advancing wavefront is obstructed by some sharp obstacle.

Classification of Diffraction

The diffraction phenomenon is broadly classified into the following two general classes.

i. Fresnel's diffraction

In this class of diffraction, the light source and the obstacle are separated by finite distance. Therefore, the wavefront incident on the obstacle is either cylindrical or spherical.

ii. Fraunhofer's diffraction

In this class of diffraction, the light source and the obstacle are separated by infinite distance. Therefore, the wavefront incident on the obstacle is plane. In the laboratory, infinite distance is created by placing a lens in between the light source and the obstacle so that the light source is at the focus of the lens.

Fresnel's Explanation of Rectilinear Propagation of Light

The greatest difficulty encountered by the supporters of the wave theory of light was how to explain the observed fact that light propagates in a straight line.

Introduction

Electromagnetic radiation scattered by an object contains all the information about the object. In photography, distribution of only the intensities of light scattered from the object are recorded on photographic plates. It is a 2-D representation of 2-D or 3-D object; it gives only a single view. The term “holography” is derived from Greek by combining Holos (whole) and graphy (writing) meaning complete recording of information on images in terms of scattered intensities and phases. In holography, distribution of intensities of light scattered from the object along with is phases are recorded on photographic plates. It is a 3-D representation of a 3-D object on a 2-D sheet; it gives a 3-D view. Here threedimensional images using coherent laser light are produced on photographic plates. Therefore, though holography was invented by Dennis Gabor in 1948 (it earned him th Nobel prize in Physics in 1971), it gained momentum only after the invention of the laser in 1960, the powerful source of coherent light. In this chapter, the concept of holography is presented very briefly.

Basic Principles of Holography

The basic principle of holography was first put forward by Dennis Gabor in 1948 while working on a project to improve the resolving power of the electron microscope. In holography, three-dimensional perspective images (the clarity of vision changes with change in eye position) are produced on a photographic film which gives a sensation of the exact original 3-D object. Here the intensities and the local propagation direction or phase is recorded on the photographic film. However, all recording films record only the variation of the intensity of the object wave (i.e., light wave scattered by the object); therefore, to record phases, we must convert the phase information into variations of intensity. This does not happen in photographic images. However, it can be achieved through the process of optical interference of the light waves. In the interference and diffraction patterns of light waves, both intensities and phases are recorded.

The basic principle of holography can be understood by referring to Fig. 14

The plane monochromatic wave of laser light, known as reference wave, is incident on a point object and is scattered by it.

Introduction

The phenomenon of electromagnetism in any medium is completely described by a set of four first order partial differential equations called Maxwell's equations. Maxwell's equations are the relationships between electric and magnetic fields in the presence of electric charges and currents, whether steady or rapidly fluctuating, in vacuum or in matter. The equations represent one of the most elegant and concise way to describe the fundamentals of electromagnetism. Maxwell's equations are a combination of the works of Gauss, Faraday, Ampère, Biot, Savart, and others. Remarkably, Maxwell's equations are perfectly consistent with the transformation equations of the special theory of relativity. To be more exact, these equations constitute a complete description of the behavior of electric and magnetic fields separately or jointly in any medium.

Vector Calculus

In vector calculus, the spatial derivatives of one types of vector and scalar fields give other types of vector or scalar fields. Depending upon the requirement, the first order differential operator (see Eq. 5.2) may be applied to a scalar function to obtain a vector function or vice versa. It may also give rise to one type of vector field from another type of vector field! The concept of vector calculus was fully exploited by James Clerk Maxwell in a simple way in discovering the missing link between the electric field and the magnetic field, thus establishing the electromagnetic nature of light. Therefore, for complete appreciation of complexities of electromagnetism, at least a brief explanation of vector calculus would be highly beneficial.

The field, in vector calculus, is defined as a region within which every physical quantity can be expressed as a continuous function of the position of a point in the region. The corresponding function is called a point function. Broadly speaking, fields are of two types – scalar fields and vector fields. All the quantities in a scalar field are scalars and all the quantities in a vector field are vectors. All quantities in both scalar and vector fields are functions of positions and times. The vectors in vector fields and the scalars in scalar fields may change with respect to positions and times. First, we shall discuss what are line integrals, surface integrals and volume integrals.

Line integrals

The integration of a vector along a curve in a vector field is called a line integral.

Science in general may be described as organized common sense. In the real world of science, nothing prevails except rationality and logics. Science does not believe in miracles. Clear understanding of the basic principles of science is essential for technological and social development. Once upon a time, the base of engineering was mainly empirical; however, now it is completely scientific. Physics is a fundamental aspect of science on which all engineering sciences have been built upon. Nowadays, more stress is given to the understanding of the basic principles rather than on remembering specific procedures. The fundamental concepts of physics have paved the way for the development of technologies. All modern technological advances from laser micro surgery to television, from computers to dishwashers to mobile phones, from remote controlled toys to space vehicles, trace back directly to the principles of physics. Accordingly, the syllabus of engineering courses includes physics as an essential ingredient.

This book, entitled Principles of Engineering Physics 1, is designed as a textbook keeping in view the engineering physics course curricula prescribed by most technical universities of India. The present book begins with oscillations and waves and ends with holography, containing altogether fourteen chapters. This book is written in a logical and coherent manner for easy understanding. The concepts of physics are mathematized without losing the beauty of the physical ideas involved. Emphasis has been given to an understanding of the basic concepts and their applications to a number of engineering problems. Each topic has been discussed in detail, both conceptually and mathematically, so that students do not face any kind of difficulties. All the derivations and solutions of numerical examples are given in detail. Each chapter contains a large number of solved numerical examples, unsolved numerical problems with answers, practical applications, theoretical questions, and multiple choice questions with answers. Certain topics and derivations that are not included directly in the syllabi have also been included in the book for the sake of continuity and completeness. The scope of the book thus has been expanded beyond the basic needs of undergraduate engineering students. We hope this book will be of immense help not only to the students but also to the teachers.

The authors sincerely request the readers for their constructive criticisms via emails [email protected] and [email protected] for future modification of the book.

Introduction

Many physical properties of solids can be understood with help of the free electron model. According to this model, the valance electrons of the constituent atoms become conduction electrons and move freely throughout the solid. The aggregates of free electrons constitute an electron gas or electron cloud. The interpretation of properties of solids by the free electron model was developed long before the advent of quantum physics, a versatile tool of physical science. The classical theory has several conspicuous successes. However, as it is natural, the simplicity of the theory puts limitation on its success. Many properties of solids like specific heats, magnetic susceptibility of solids, superconductivity and the like cannot be explained by the classical theory of free electron model. With the advent of quantum physics, almost all the properties of solids could be explained in minute detail. Here the electron gas is subjected to Pauli's exclusion principle and Fermi–Dirac statistics instead of Maxwell–Boltzmann statistics as in classical theory. This new formulation constitutes the quantum theory of free electrons.

The free electron model of metals gives us a good insight into the heat capacity, thermal and electrical conductivity, susceptibility and electrodynamics of metals. However, the model fails to explain the distinction between metals, semi-metals (materials with a very small overlap between the bottom of the conduction band and the top of the valence band), semiconductors and insulators; the occurrence of positive values of Hall coefficient; the relation between conduction electrons in the metal and the valence electrons of free atoms and many transport properties of solids. The band theory of solids, a simple theory, then was developed to account for all these facts. We shall apply these theories to explain a few properties of solids in detail as far as the scope of this book permits.

Free Electron Theory of Metals

Metals are generally characterized by high electrical conductivity and thermal conductivity. Many of the special properties of metals are attributed to valence electrons. Valence electrons are free to move throughout the solid and constitute the electron gas or electron cloud or simply Fermi gas. In the free electron theory, the fundamental postulate is that potential field due to ion cores is uniform throughout the solid. The potential energy value is negative since there is a force of attraction between the positive ion cores and electrons.

From time immemorial, mankind has manipulated specific properties of materials for specific self-benefits. A clear understanding of the basic principles of materials science is essential for technological development. The rapid development of materials science resulted in the invention of miniature electronic devices. All modern technologically advanced devices are directly related to an understanding of materials at the atomic and sub-atomic levels. Accordingly, the technical universities throughout the world include materials science as an essential ingredient in their course curricula.

Materials science is an interdisciplinary subject relying heavily on basic principles of physics and chemistry. Electrical and thermal conductivity, dielectric constant, magnetization, optical reflection and refraction, strength and toughness etc. are properties that originate from the internal structures of the materials. The present book, entitled Principle of Engineering Physics 2, contains chapters mostly related to materials science. It is designed as a textbook, keeping in view the engineering physics and materials science course curricula prescribed by most technical universities of India. It begins with ‘Crystal Structure’ and ends with ‘Nano Structure & Thin Films’, containing altogether thirteen chapters. The book is written in a logical and coherent manner for easy understanding by students. It presumes a working knowledge of quantum mechanics, optics, electricity and magnetism. Emphasis has been given to an understanding of the basic concepts and their applications to a number of engineering problems. Each topic is discussed in detail both conceptually and mathematically, so that students will not face comprehension difficulties. Derivations and solutions of numerical examples are also provided in detail. Each chapter contains a large number of solved numerical examples, unsolved numerical problems with answers, practical applications, theoretical questions, and multiple choice questions with answers. Certain topics and derivations which are not present in university syllabi have been included in the book for the sake of continuity and completeness. The scope of the book has thus been expanded beyond the basic needs of undergraduate engineering students. We hope, this book will be helpful not only to the students but also to the teachers.

In spite of utmost care, some typographical errors might have inadvertently crept into the book. Readers would be highly appreciated if they convey these errors to the authors. The authors sincerely request the readers for their constructive criticisms via emails [email protected] and [email protected] for future modification of the book.